I'd recommend using Magento's data migration tool for Magento 1 - Magento 2; it should move over the customer information for you, along other information as well. I believe that Magento 2 is using SHA256 and also support MD5 for password hashing for customer passwords.

However, if you're curious, you could try just copy-pasting the encrypted passwords from one server to the next, and see if it works. I would recommend doing this on a test environment, and making sure that you back up the data. I've done this for a Magento 1 to Magento 1 site.